Title :

Adaptive goodness-of-fit testing from indirect observations

Author(s) :

Butucea, Cristina [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Matias, Catherine [Auteur correspondant]
Laboratoire Statistique et Génome [LSG]
Pouet, Christophe [Auteur]
Laboratoire d'Analyse, Topologie, Probabilités [LATP]

Journal title :

Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques

Pages :

352-372

Publisher :

Institut Henri Poincaré (IHP)

Publication date :

2009

ISSN :

0246-0203

English keyword(s) :

Adaptive nonparametric tests
Convolution model
Goodness-of-fit tests
Infinitely differentiable functions
Partially known noise
Quadratic functional estimation
Sobolev classes
Stable laws

HAL domain(s) :

Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

In a convolution model, we observe random variables whose distribution is the convolution of some unknown density $f$ and some known noise density $g$. We assume that $g$ is polynomially smooth. We provide goodness-of-fit ...
Show more >In a convolution model, we observe random variables whose distribution is the convolution of some unknown density $f$ and some known noise density $g$. We assume that $g$ is polynomially smooth. We provide goodness-of-fit testing procedures for the test $H_0:f=f_0$, where the alternative $H_1$ is expressed with respect to $\mathbb{L}_2$-norm (\emph{i.e.} has the form $\psi_{n}^{-2}\|f-f_0\|_2^2 \ge \mathcal{C}$). Our procedure is adaptive with respect to the unknown smoothness parameter $\tau$ of $f$. Different testing rates ($\psi_n$) are obtained according to whether $f_0$ is polynomially or exponentially smooth. A price for adaptation is noted and for computing this, we provide a non-uniform Berry-Esseen type theorem for degenerate $U$-statistics. In the case of polynomially smooth $f_0$, we prove that the price for adaptation is optimal. We emphasise the fact that the alternative may contain functions smoother than the null density to be tested, which is new in the context of goodness-of-fit tests.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL